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Control Randomisation Approach for Policy Gradient and Application to Reinforcement Learning in Optimal Switching 政策梯度的控制随机化方法及其在最优切换强化学习中的应用
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-12-16 DOI: 10.1007/s00245-024-10207-5
Robert Denkert, Huyên Pham, Xavier Warin
{"title":"Control Randomisation Approach for Policy Gradient and Application to Reinforcement Learning in Optimal Switching","authors":"Robert Denkert,&nbsp;Huyên Pham,&nbsp;Xavier Warin","doi":"10.1007/s00245-024-10207-5","DOIUrl":"10.1007/s00245-024-10207-5","url":null,"abstract":"<div><p>We propose a comprehensive framework for policy gradient methods tailored to continuous time reinforcement learning. This is based on the connection between stochastic control problems and randomised problems, enabling applications across various classes of Markovian continuous time control problems, beyond diffusion models, including e.g. regular, impulse and optimal stopping/switching problems. By utilizing change of measure in the control randomisation technique, we derive a new policy gradient representation for these randomised problems, featuring parametrised intensity policies. We further develop actor-critic algorithms specifically designed to address general Markovian stochastic control issues. Our framework is demonstrated through its application to optimal switching problems, with two numerical case studies in the energy sector focusing on real options.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
CAT(0) and cubulated Shephard groups
IF 1 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2024-12-16 DOI: 10.1112/jlms.70050
Katherine M. Goldman
{"title":"CAT(0) and cubulated Shephard groups","authors":"Katherine M. Goldman","doi":"10.1112/jlms.70050","DOIUrl":"https://doi.org/10.1112/jlms.70050","url":null,"abstract":"<p>Shephard groups are common generalizations of Coxeter groups, Artin groups, and graph products of cyclic groups. Their definition is similar to that of a Coxeter group, but generators may have arbitrary order rather than strictly order 2. We extend a well-known result that Coxeter groups are <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>CAT</mi>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{CAT}(0)$</annotation>\u0000 </semantics></math> to a class of Shephard groups that have ‘enough’ finite parabolic subgroups. We also show that in this setting, if the associated Coxeter group is type (FC), then the Shephard group acts properly and cocompactly on a <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>CAT</mi>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{CAT}(0)$</annotation>\u0000 </semantics></math> cube complex. As part of our proof of the former result, we introduce a new criteria for a complex made of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mn>3</mn>\u0000 </msub>\u0000 <annotation>$A_3$</annotation>\u0000 </semantics></math> simplices to be <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>CAT</mi>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{CAT}(1)$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70050","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral influence in networks: an application to input-output analysis 网络中的频谱影响：投入产出分析的应用
IF 1 4区 数学
Journal of Combinatorial Optimization Pub Date : 2024-12-16 DOI: 10.1007/s10878-024-01244-5
Nizar Riane
{"title":"Spectral influence in networks: an application to input-output analysis","authors":"Nizar Riane","doi":"10.1007/s10878-024-01244-5","DOIUrl":"https://doi.org/10.1007/s10878-024-01244-5","url":null,"abstract":"<p>This paper introduces the concepts of spectral influence and spectral cyclicality, both derived from the largest eigenvalue of a graph’s adjacency matrix. These two novel centrality measures capture both diffusion and interdependence from a local and global perspective respectively. We propose a new clustering algorithm that identifies communities with high cyclicality and interdependence, allowing for overlaps. To illustrate our method, we apply it to input-output analysis within the context of the Moroccan economy.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"85 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142832114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relating code equivalence to other isomorphism problems 将代码等价与其他同构问题联系起来
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-12-16 DOI: 10.1007/s10623-024-01542-3
Huck Bennett, Kaung Myat Htay Win
{"title":"Relating code equivalence to other isomorphism problems","authors":"Huck Bennett, Kaung Myat Htay Win","doi":"10.1007/s10623-024-01542-3","DOIUrl":"https://doi.org/10.1007/s10623-024-01542-3","url":null,"abstract":"<p>We study the complexity of the <i>Code Equivalence Problem</i> on linear error-correcting codes by relating its variants to isomorphism problems on other discrete structures—graphs, lattices, and matroids. Our main results are a fine-grained reduction from the Graph Isomorphism Problem to the Linear Code Equivalence Problem over any field <span>(mathbb {F})</span>, and a reduction from the Linear Code Equivalence Problem over any field <span>(mathbb {F}_p)</span> of prime, polynomially bounded order <i>p</i> to the Lattice Isomorphism Problem. Both of these reductions are simple and natural. We also give reductions between variants of the Code Equivalence Problem, and study the relationship between isomorphism problems on codes and linear matroids.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"2021 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142832039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Fourier multiplier theorem on anisotropic Hardy spaces associated with ball quasi-Banach function spaces 与球准巴纳赫函数空间相关的各向异性哈代空间上的傅里叶乘数定理
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-12-16 DOI: 10.1007/s43034-024-00396-z
Xianjie Yan, Hongchao Jia, Dachun Yang
{"title":"A Fourier multiplier theorem on anisotropic Hardy spaces associated with ball quasi-Banach function spaces","authors":"Xianjie Yan,&nbsp;Hongchao Jia,&nbsp;Dachun Yang","doi":"10.1007/s43034-024-00396-z","DOIUrl":"10.1007/s43034-024-00396-z","url":null,"abstract":"<div><p>Let <i>A</i> be a general expansive matrix. Let <i>X</i> be a ball quasi-Banach function space on <span>(mathbb {R}^n)</span>, which supports both a Fefferman–Stein vector-valued maximal inequality and the boundedness of the powered Hardy–Littlewood maximal operator on its associate space. The authors first establish the boundedness of convolutional anisotropic Calderón–Zygmund operators on the Hardy space <span>(H_X^A(mathbb {R}^n))</span>. As an application, the authors also obtain the boundedness of Fourier multipliers satisfying anisotropic Mihlin conditions on <span>(H_X^A(mathbb {R}^n))</span>. All these results have a wide range of applications; in particular, when they are applied to Lebesgue spaces, all these results reduce back to the known best results and, even when they are applied to Lorentz spaces, variable Lebesgue spaces, Orlicz spaces, Orlicz-slice spaces, and local generalized Herz spaces, the obtained results are also new.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cubulating surface-by-free groups
IF 0.8 2区 数学
Journal of Topology Pub Date : 2024-12-16 DOI: 10.1112/topo.70011
Mahan Mj
{"title":"Cubulating surface-by-free groups","authors":"Mahan Mj","doi":"10.1112/topo.70011","DOIUrl":"https://doi.org/10.1112/topo.70011","url":null,"abstract":"<p>Let\u0000\u0000 </p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"17 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multi-indice B $B$ -series
IF 1 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2024-12-16 DOI: 10.1112/jlms.70049
Yvain Bruned, Kurusch Ebrahimi-Fard, Yingtong Hou
{"title":"Multi-indice \u0000 \u0000 B\u0000 $B$\u0000 -series","authors":"Yvain Bruned,&nbsp;Kurusch Ebrahimi-Fard,&nbsp;Yingtong Hou","doi":"10.1112/jlms.70049","DOIUrl":"https://doi.org/10.1112/jlms.70049","url":null,"abstract":"<p>We propose a novel way to study numerical methods for ordinary differential equations in one dimension via the notion of multi-indice. The main idea is to replace rooted trees in Butcher's <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math>-series by multi-indices. The latter were introduced recently in the context of describing solutions of singular stochastic partial differential equations. The combinatorial shift away from rooted trees allows for a compressed description of numerical schemes. Furthermore, such multi-indices <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math>-series uniquely characterize the Taylor expansion of 1-dimensional local and affine equivariant maps.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Boson-fermion Realization of Highest Weight Modules over (mathfrak{g}widetilde{mathfrak{l}_{M/N}}(theta))
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-12-15 DOI: 10.1007/s10114-024-3583-2
Fu Lin Chen, Xin Huang, Shao Bin Tan
{"title":"A Boson-fermion Realization of Highest Weight Modules over (mathfrak{g}widetilde{mathfrak{l}_{M/N}}(theta))","authors":"Fu Lin Chen,&nbsp;Xin Huang,&nbsp;Shao Bin Tan","doi":"10.1007/s10114-024-3583-2","DOIUrl":"10.1007/s10114-024-3583-2","url":null,"abstract":"<div><p>In this paper, we construct a superfermionic representation as well as a vertex representation for twisted general linear affine Lie superalgebras. We also establish a module isomorphism between them, which generalizes the super boson-fermion correspondence of type <i>B</i> given by Kac-van de Leur. Based on this isomorphism, we determine explicitly the irreducible components of these two representations. Particularly, we obtain in this way two kinds of systematic construction of level 1 irreducible integrable highest weight modules for twisted general linear affine Lie superalgebras.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 12","pages":"2879 - 2903"},"PeriodicalIF":0.8,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Life Span of Classical Solutions to Nonlinear Wave Equations with Weighted Terms in Three Space Dimensions
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-12-15 DOI: 10.1007/s10114-024-2600-9
Hu Sheng Wang, Fan Lü
{"title":"The Life Span of Classical Solutions to Nonlinear Wave Equations with Weighted Terms in Three Space Dimensions","authors":"Hu Sheng Wang,&nbsp;Fan Lü","doi":"10.1007/s10114-024-2600-9","DOIUrl":"10.1007/s10114-024-2600-9","url":null,"abstract":"<div><p>The paper considers the Cauchy problem with small initial values for semilinear wave equations with weighted nonlinear terms. Similar to Strauss exponent <i>p</i><sub>0</sub>(<i>n</i>) which is the positive root of the quadratic equation <span>(1+{1over 2}(n+1)p-{1over 2}(n-1)p^{2}=0)</span>, we get smaller critical exponents <i>p</i><sub><i>m</i></sub>(<i>n</i>),<i>p</i><span>\u0000 <sup>*</sup><sub><i>m</i></sub>\u0000 \u0000 </span>(<i>n</i>) and have global existence in time when <i>p</i>&gt;<i>p</i><sub><i>m</i></sub>(<i>n</i>) or <i>p</i>&gt;<i>p</i><span>\u0000 <sup>*</sup><sub><i>m</i></sub>\u0000 \u0000 </span>(<i>n</i>). In addition, for the blow-up case, the introduction of the spacial weight shows the optimality of new upper and lower bound.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 12","pages":"2984 - 3002"},"PeriodicalIF":0.8,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A novel active learning method based on the anisotropic kernel density estimation for global metamodeling in support of engineering design
IF 3.9 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-12-15 DOI: 10.1016/j.cnsns.2024.108530
Jiaxing Wang, Wei Zhao, Xiaoping Wang, Yangyang Chen, Xueyan Li
{"title":"A novel active learning method based on the anisotropic kernel density estimation for global metamodeling in support of engineering design","authors":"Jiaxing Wang, Wei Zhao, Xiaoping Wang, Yangyang Chen, Xueyan Li","doi":"10.1016/j.cnsns.2024.108530","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108530","url":null,"abstract":"In modern engineering practice, there is a steady increase in the need for multi-dimensional global approximations of complex black-box functions involved in today's engineering design problems. Metamodels have been proved to be effective alternatives for analyzing and predicting highly complex original models at a lower computational cost. The Kriging model is valued for its ability to predict the uncertainty of unknown points, which makes it widely used in the active learning methods for global approximation. However, these methods do not extend well to other metamodeling methods. This paper proposes an anisotropic kernel density estimation-based global fit (AKDGF) criterion for the active learning of metamodel. The AKDGF consists of two terms: global exploration dependent on the anisotropic kernel density (AKD) estimation and local development for larger nonlinear regions, which can be combined with various metamodeling methods. The initial sample set should be uniformly distributed in the design space as evenly as possible. Therefore, the uniform design approach is utilized to select the initial sample set for building the metamodel, and the AKDGF selects samples with high expected improvements to the metamodel to update the DOE sequentially. Five numerical examples and three engineering examples are presented to illustrate the proposed method and prove its good performance.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"14 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142849251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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